Natural patterns such as fractals, spirals or tessellations have intrigued mathematicians and biologists for decades. These evolutionary conserved structures emerge from the physical properties of the soft living matter. Geometrical concepts have been widely applied as an approach to understand the basis of tissue architecture and remodelling. A clear example is the stereotyped polygon distribution found in very diverse proliferating epithelia among metazoans. Currently, it is accepted that the conserved distribution is a mathematical consequence of cell divisions, via a probabilistic Markov chain, in conjunction with cell arrangements. We have used simple geometric concepts based in Voronoi tessellations to investigate the organization of diverse tissues from Drosophila epithelia to human muscles. We show that the conserved polygon distribution is not exclusive to proliferating tissues. On the contrary, the packing of a “relaxed” Voronoi tessellations and non-proliferative polygonal tissues present the stereotyped distribution. Our results demonstrate that the distribution of cell areas dictates the frequency of polygons in these tissues. The increase of cell size heterogeneity deviate the tissue from the conserved polygon distribution. We will present real and simulated data that explain the physical nature of this cellular constraint that is able to drive the organization of diverse tissue structures.

Trabajo presentado en el XII Symposium on Bioinformatics (XII Jornadas de Bioinformática), celebrado en Sevilla del 21 al 24 de septiembre de 2014.

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